Group ramsey theory

A subset S of a group G is said to be a sum-free set if $\text{S ∩ (S + S) = ?}$. Such a set is maximal if for every sum-free set T ? G, we have |T| ? |S|. Here, we generalize this concept, defining a sum-free set S to be locally maximal if for every sum free set T such that S ? T ? G, we have S = T. Properties of locally maximal sum-free sets are studied and the sets are determined (up to isomorphism) for groups of small order.